From the given information we can write the following equation:
Perimeter: \(P = 2(l + w) = 24 meters\)
Area: \(A = l \times w = 32 square meters\)
From the perimeter equation, we can express \(l + w\) as:
$$l + w = \frac{24}{2} = 12 meters$$
Substituting the expression \(l + w = 12 meters\) into the area equation:
$$l \times w = 32 square meters$$
$$l \times (12 - l) = 32 square meters$$
$$12l - l^2 = 32 square meters$$
Rearranging the equation into the standard quadratic equation form:
$$l^2 - 12l + 32 = 0$$
Solving the quadratic equation for \(l\):
$$(l - 8)(l - 4) = 0$$
$$l_1 = 8 meters, l_2 = 4 meters$$
Since the length cannot be less than the width, we will consider \(l = 8 meters\) and \(w = 4 meters\).
Therefore, the length is \(8\) meters and the width is \(4\) meters.